what moves the river
the forces behind emotional dynamics
in the previous post i used the river metaphor to illustrate the way emotions move, and to introduce the idea that dynamics are a natural part of that movement. this post looks at the forces behind those dynamics.
the framework i’ve made borrows from dynamical systems, which are systems that use a set of rules to describe how something changes over time. the visuals use a core formula that defines the basic forces behind emotional activation over time. the interaction of these forces is where everything else comes from, like patterned movement and the outcomes that may emerge.
for a river, the forces behind its motion are many, but they include gravity, pressure, friction and inertia. for emotional dynamics, i settled on a simple set of forces that, from my own perspective, describe and govern the different types of motion emotional activation takes.
in words, the formula is roughly: change in activation = settling + spreading + direction + attractor + noise. you’ll see me refer to “the map” below. for now, think of it as the space activation moves around in. there’s more to it than that, and i’ll get into how it’s built in a later post. here are the five i landed on:
settling (containment γ: the pull back toward baseline)
what it does. zero here means baseline, your resting level of activation. wherever activation is above zero, γ pulls it down. wherever it’s below zero, γ pulls it up. the pull is proportional to the distance from zero, so twice as far out means twice the pull.
in the river. after a surge of rain the water rises, then gradually drops back to its usual level. the higher it rose, the faster it falls at first.
in life. after an argument, your heart rate and your thoughts gradually come back down, even if nothing gets resolved.
spreading (diffusion κ: spreading to neighbours)
what it does. each spot on the map gets nudged toward the average of the spots around it. peaks flatten, dips fill in, and a sharp spike becomes a wider, lower hump.
in the river. where a warm spring feeds into a cold river, the warmth doesn’t stay in one spot. it mixes outward into the water around it, the patch growing wider and less warm, until the difference is barely noticeable.
in life. a stressful morning at work that leaks into how you feel about the commute, dinner, and the rest of the evening, getting milder as it goes.
direction (drift G: carrying activation along)
what it does. G carries activation along a direction on the map, the way a current carries something floating in it. the pattern moves; it isn’t just pulled toward a point.
in the river. think of it as the slope of the river. over a steep slope activation moves faster, over a flatter slope it eases, and the direction is what tells it where it’s going.
in life. a feeling that seems to head somewhere on its own, like irritation sliding into sadness, or nervousness turning into excitement.
attractor (basin λ: the pull toward a target)
what it does. the attractor pulls activation toward it and represents return-to-theme: activation that keeps getting drawn back toward a particular meaning, theme or state. it’s a major force in the emergence of repetitive emotional patterns.
in the river. small whirlpools that create an almost mini gravitational force. within its reach, it draws activation toward a particular level, strongest at its centre and gradually weakening further out. where the current carries things along, the whirlpool keeps bringing them back around.
in life. a theme you keep circling back to, like a worry about being left out that small, unrelated moments seem to land on.
volatility (noise σ: random kicks)
what it does. noise gives activation small random kicks, up or down, with no pattern and no memory. it doesn’t depend on the current state; it just jostles. it represents the many environmental and internal stimulations that happen moment to moment, enough to stir some activation but not enough to trigger a full episode or event.
in the river. wind on the surface. small waves may form, but they don’t change the overall flow in any meaningful way. most of the time, anyway. if something is already drifting near the edge of a whirlpool, a small push from the wind can be enough to tip it in.
in life. a song, a smell, a stranger’s expression on the street. small things that nudge your mood a little and then pass.
on their own, each of these is pretty simple, and i’ll go deeper into each one in later posts. what gets interesting is what happens when they act together, and that’s where a lot of what comes later in this series starts.